Transcript Rotational Motion

Bellringer:
What would be the net acceleration of a
15 g toy car down a 30 degree incline if
the acceleration due to friction is 1.8
m/s2? Include a free-body diagram of all
forces.
Chapter 8 – Angular motion, torque, and moment of
inertia
Angular Motion

What is angular motion?
 How is it different from linear motion?
Vocabulary
Revolution
 Radian
 Angular displacement
 Angular velocity
 Angular acceleration

Equations
1 revolution = 2π radians
 Angular displacement (Θ, in rad)

 Θ = d/r (linear distance in m / radius)

Angular velocity (ω, in rad/s)
 ω = Θ/t (also equal to v/r)

Angular acceleration (α, in rad/s2)
 α = ω/t (also equal to a/r)
Practice p.200 (1-3)

Keep answers to number 1 in terms of π
Bellringer




What is the equation to convert from linear
distance to angular displacement?
What is the equation to convert from linear velocity
to angular velocity?
What is the equation to convert from linear
acceleration to angular acceleration?
 WHAT IS SIMILAR IN ALL OF THESE
EQUATIONS?
Write out the equations to find angular velocity and
to find angular acceleration.
 WHAT DO YOU NOTICE ABOUT THESE
EQUATIONS?
Torque

What is torque?
 Definition
 Equation
 Lever arm (perpendicular distance from the axis
of rotation to the point where the force is exerted)
○ L = r sin Θ when the angle is not perpendicular
Practice p.203 (11-15)
11. τ = 35 Nm, L = 25 cm, F = ?
12. 0.407 m
13. 36.6o
14. 94 Nm
15.
Net Torque

To find net torque,
use the equation:
τ = Fg r

Use net torque when you
have a situation with a
center fulcrum and 2 lever
arms
Practice p.205 (16-20)
16.mA = 43 kg, rA = 1.8 m, mS = 52 kg, rS =
?
17. 2.7 Nm
18. 0.056 kg
19. 0.042 kg
20. 789 N
Moment of Inertia
Definition
 Equation
 Compare and contrast the different
moments of inertia for various objects in
Table 8-2.

 What object would have the highest?
Lowest?
 What does this mean about this object?
Practice p.208 (21 and 24)
Units for moment of inertia are kgm2.
21. What is the change in I when r is
increased from 0.3 m to 0.6 m?
24.
Newton’s Second Law for
Rotational Motion

What is Newton’s Second Law?

How does it change with rotational
motion?
Practice p.210 (27)